Question

If an=24, which recursive formula could represent the sequence below? ...,24,88, 664, 8408A) An=(An-2)^2 + An-1 ; A1=2B) An= 3An-1 + 16; A1=16C) An= (n)An-1 - 8; A1=4D An=2An-2 + 7An-1; A1=2

Answer 1

its a on edge

Explanation:

Answer 2

When we substitute
`n = 4`, we get...

`a_(n-3)=a_1\\ \\ a_(n-2)=a_2\\ \\ a_(n-1)=a_3\\ \\ a_n=a_4`

Comparing the given sequence: 24, 88, 664, 8408, we get

`a_(n-3)=a_1=24\\ \\ a_(n-2)=a_2=88\\ \\ a_(n-1)=a_3=664\\ \\ a_n=a_4=8408`

We need to substitute the above values in each option and check which is TRUE.

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Option A

`a_n=(a_(n-2))^2+a_(n-1), a_1=2\\ \\ a_n=(88)^2+664=7744+664\\\\a_n=8408 (TRUE)`

Option B

`a_n=3a_(n-1)+16\\ \\ a_n=3(664)+16\\\\a_n=2008 (FALSE)`

Option C

`image`

Option D

`a_n=2a_(n-2)+7a_(n-1)\\ \\ a_n=2(88)+7(664)\\ \\ a_n=4824(FALSE)`

Conclusion:

Option A is the correct answer.